RBFPUM with QR Factorization for Solving Water Flow Problem in Multilayered Soil

Abstract

AbstractWe discuss the numerical modeling of infiltration in variably-saturated porous media. Richards’ equation is used to describe the infiltration towards the water table. It is difficult to accurately approximate its solution especially when we deal with layered soil due to its highly nonlinear fact. In this work, the nonlinearity is handled by using Gardner model. In the case of homogeneous soil, the linearized equation is solved using radial basis function partition of unity method (RBFPUM) with the introduction of QR factorization of Gaussian in order to enhance the numerical solution for small values of the so-called “shape parameter.” In the case of layered soil, domain decomposition principle is introduced. It is based on decomposing the general problem into many subproblems. The latter are solved by RBFPUM-QR and patched by using the Steklov–Poincaré equation. Infiltration towards water table in homogeneous and layered soil is considered as a numerical test.